Continuous Phase Modulation (CPM) is a known method for transmitting symbols (information) such as numbers, text messages and encoded voice messages in digital communications systems. A CPM signal is a modulated signal characterized by a phase shift function incorporated with a modulation index. In order to have smooth phase transition in the modulated signal's carrier and reduce spectral side lobes, a partial response CPM signal with phase shift function that has a non-constant duration larger than one symbol duration is often used. Ideally, a receiver for demodulating this partial response CPM signal includes a maximum-likelihood sequence detector implemented using a bank of matched-filters followed by a Viterbi processor. However, the receiver requires relatively large number of filters and trellis states resulting in undesirable computational demands.
Efforts have been made to reduce the complexity of receivers for demodulating CPM signals. One approach is based on the decomposition of a CPM signal into a sum of pulse amplitude modulated (PAM) pulses. It has been found that a significant reduction in the number of both matched-filters and trellis states can be achieved by using only a few main pulses to approximate the CPM signal. The conventional decomposition process is based on Laurent decomposition which is only valid for binary CPM signals with a non-integer modulation index. CMP signals with an integer modulation index can be treated as the product of two CPM signals with non-integer modulation indexes. However, because the decomposition of an integer into two non-integer values is not unique, different decomposition of the modulation index will lead to different expressions of the same CPM signal.
Another conventional method to demodulate CPM signals is by using a frequency discriminator associated with real and imaginary demodulators that provide a complex baseband signal S(t) with real and imaginary components. Typically, the frequency discriminator multiplies the baseband signal S(t) by a conjugated delayed version of the baseband signal S*(t−Δt) with time delay Δt to provide a processed signal S(t)·S*(t−Δt). The imaginary part of the processed signal S(t)·S*(t−Δt) is extracted to provide a decision variable that is processed, by a decision module, to provide a decision indicating what symbol was most likely modulated in the baseband signal S(t). From this decision, a symbol is provided at the output of the discriminator and thereafter further decisions provide further symbols as will be apparent to a person skilled in the art.
In a conventional frequency discriminator, the decision module assumes that there is a linear relationship between decision variable and the carrier phase difference. However, this relationship is actually sinusoidal. There is also inherent noise in the frequency discriminator that affects decision accuracy. Furthermore, decision accuracy may also be affected by center frequency drift and symbol timing that can lead to error propagation.
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